Multiparty Pure State Entanglement And Its Application In Quantum Communication

"Entanglement" is the essence of quantum mechanics, the entanglement of multipartite quantum pure states can achieve a lot of task which classical information theory could not successful, such as quantum teleportation, quantum secure direct communication, quantum remote state of preparation , quantum secret sharing and so on.Quantum entanglement is the most important physical resource in quantum information and quantum compute. After 80 years of entanglement was proposed, people continue to explore the phenomenon of entanglement, and made great progress, such as Bell inequality and CHSH inequality. But we are still not fully understood its essence, such as its mathematical structure. For a given quantum state, how to determine whether it is entangled? Furthermore, how to measure the degree of entanglement of a quantum state? further, how to use quantum entanglement to better complete quantum information transfer tasks? Many problems still need research in future.The physical resource for quantum entanglement is made more achievements in quantum communication. Quantum teleportation can use the quantum entanglement to teleport information taking quantum states of microcosmic particles as carriers of information. The information of the original can generate quantum information and classical information. Quantum Teleportation needs quantum channel and classical channel to transfer quantum and classical information respectively. The classical information is extracted by the sender after her measurement on the original, and the remaining of the original is quantum information. According to the quantum and classical information, the receiver can reconstruct the original on the other particles. In quantum teleportation, the quantum state of the original is teleported, but the original is stay in the sender, and the sender know nothing about the quantum state she sent to the receiver. The quantum state is collapsed since the sender make her measurement. Quantum teleportation plays an important role in quantum computation and quantum communication. Since Bennett et. al. has proposed a scheme to teleportation an unknown quantum state via classical and quantum Einstein-Podolsky-Rosen(EPR) channel in 1993, much attention has been paid to quantum teleportation.The quantum teleportation is different to quantum remote state preparation. Quantum remote state preparation can be realized in some case when quantum teleportation can not be implement, which has great application value. Compared with quantum teleportation, information are completely known to sender in quantum remote state preparation, i.e., the coefficient and phase information, the sender according to known the information of coefficient and phase to construct a complete orthogonal basis to measure system, so as to achieve the purpose of transmitting information. It is difficult to construct the orthogonal complete basis along with the increase of number of particle, the success of communication decreased, it can achieve 50% only in some special cases, and special situation can reach 100%. We use the coefficients and phase separation to construct the orthogonal complete basis, so that the success rate of the communication can reach 1 for any particle state.